On improving the accuracy of Horner's and Goertzel's algorithms

Details On improving the accuracy of Horner's and Goertzel's algorithms On improving the accuracy of Horner's and Goertzel's algorithms

2004-07-12

arxiv.org/abs/math/0407177v1

Mathematics

Numerical Analysis

22 pages, 3 figures, presented on the GAMM Meeting, Brunschweig, September 2003

Scientific paper

10.1007/s11075-004-4570-4

It is known that Goertzel's algorithm is much less numerically accurate than the Fast Fourier Transform (FFT)(Cf. \cite{gen:69}). In order to improve accuracy we propose modifications of both Goertzel's and Horner's algorithms based on the divide-and-conquer techniques. The proof of the numerical stability of these two modified algorithms is given. The numerical tests in Matlab demonstrate the computational advantages of the proposed modifications. The appendix contains the proof of numerical stability of Goertzel's algorithm of polynomial evaluation.

Affiliated with

Also associated with

No associations

Rating

On improving the accuracy of Horner's and Goertzel's algorithms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On improving the accuracy of Horner's and Goertzel's algorithms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On improving the accuracy of Horner's and Goertzel's algorithms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-58359